During closed-loop induction of anesthesia a closed-loop system will typically administer propofol to bring a patient to a target depth of hypnosis, or reference point, as quickly as possible while minimizing overshoot. Infusion rates are modified in response to patient feedback to maintain the patient at the reference point. In many cases, rapid inductions may be ideal. In some populations and contexts, however, slower inductions may be preferable and result in better patient outcomes. We introduce a framework for explicitly defining and optimizing clinical outcomes of interest during closed-loop inductions. The central innovation is to replace the traditional fixed reference point with a parametric, time-varying reference function. The parameters of the reference function are then selected to minimize an objective function that encapsulates a clinical goal for the population. We consider as objectives 1) combinations of over- and under-shoot of the target depth of hypnosis, 2) time to stably reach the target, and 3) the amount of propofol administered. By incorporating population variability in the objective function, the resulting reference function defines an optimal dosing protocol for a specific outcome in the target population. We illustrate this approach by simulating closed-loop inductions for a constructed population of synthetic patients. The population is split into training and test sets that are used to identify and evaluate optimal reference functions, respectively. Reference function performance is compared to a standard approach of targeting a fixed reference point, corresponding to a rapid-induction strategy. The outcome of interest was almost always minimized in the test set by use of a reference function with less variability between patients. Our simulations suggest that reference functions can be an effective method of achieving clinical goals when induction speed is not the only priority.
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